It always amuses me that when they don't know what is/was there, they always refer to it as a "secret nuclear bunker", what ever that might be. Coal bunker, golf course bunker ?
I think what they mean is a bunker in the wartime sense of the term, i.e. a command and control centre. I have a feeling Churchill may have introduced the term, but I could be wrong.
Parts of the miles of tunnels deep under the ground near Corsham, where Bath Stone had been quarried out since early Victorian times, were developed during the height of Cold War paranoia as a control centre for the Government should the unimaginable actually happen, and it's remained the mothballed (and thankfully unused) ever since. So in that sense I suppose it is a "Secret" and "Nuclear" "Bunker".
It's been decommissioned now, but still isn't open to the public. The air temperature and humidity is completely stable down there so nothing rusts or rots, and looking around the place is like walking into a time capsule. There's living accomodation, kitchens, stores, a hospital; everything a few hundred people would need to live for months if necessary undergound (including vast lakes of pure water, now gradually reclaiming many of the smaller quarries)
I was last down there just a couple of months ago and took this photo (amongst many more) of the telephone exchange which formed part of the emergency command and control centre. Quite who the operators down there were supposed to speak to above ground in the aftermath of a nuclear holocaust is unclear, since presumably everyone else would have been wiped out. It's one of the old style "plug and socket" type exchanges. Note how the chairs still have their protective paper wrapping, just as they were delivered from the factory. The telephone directories were last updated in 1967.